Translating vertices orthographically
You can use snapping with the increment option. The transformations will snap to the grid. By using the manipulators you can select the axis for the transformation.



The snapping is determined by the size of the grid. 

By zooming in or out on orthographic view you can determine the precision of the transformation.



Alternatively you can is change the scale for the grid.

Press N and go to Display. In the scale section you can change the size of the grid and the snapping precision will be changed along with it.



On top of that you can determine the transformations numerically for example: if you want to move sometning 2.5 units on the X axis you'd type G  X
 2 . 5